# FaithRL: Learning to Reason Faithfully through Step-Level Faithfulness Maximization

arXiv: https://arxiv.org/abs/2602.03507 · HTML: https://mlsanity.com/paper/2602.03507/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 21 of 21)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Beyond Binary Rewards: Training LMs to Reason About Their Uncertainty](https://mlsanity.com/paper/2507.16806/) (2025)
- [Making Reasoning Matter: Measuring and Improving Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2402.13950/) (2024)
- [Faithfulness vs. Plausibility: On the (Un)Reliability of Explanations from Large Language Models](https://mlsanity.com/paper/2402.04614/) (2024)
- [Can AI Assistants Know What They Don't Know?](https://mlsanity.com/paper/2401.13275/) (2024)
- [Detection and Mitigation of Hallucination in Large Reasoning Models: A Mechanistic Perspective](https://mlsanity.com/paper/2505.12886/) (2025)
- [TruthRL: Incentivizing Truthful LLMs via Reinforcement Learning](https://mlsanity.com/paper/2509.25760/) (2025)
- [KnowHalu: Hallucination Detection via Multi-Form Knowledge Based Factual Checking](https://mlsanity.com/paper/2404.02935/) (2024)
- [A Comprehensive Survey on Trustworthiness in Reasoning with Large Language Models](https://mlsanity.com/paper/2509.03871/) (2025)
- [Learning to Reason for Factuality](https://mlsanity.com/paper/2508.05618/) (2025)
- [KnowRL: Exploring Knowledgeable Reinforcement Learning for Factuality](https://mlsanity.com/paper/2506.19807/) (2025)
- [Improving Contextual Faithfulness of Large Language Models via Retrieval Heads-Induced Optimization](https://mlsanity.com/paper/2501.13573/) (2025)
- [Is That Your Final Answer? Test-Time Scaling Improves Selective Question Answering](https://mlsanity.com/paper/2502.13962/) (2025)
- [Joint Evaluation of Answer and Reasoning Consistency for Hallucination Detection in Large Reasoning Models](https://mlsanity.com/paper/2506.04832/) (2025)
- [Hallucination-aware Optimization for Large Language Model-empowered Communications](https://mlsanity.com/paper/2412.06007/) (2024)

## Built on by (most cited first, 4 of 4)

- [SAT: Balancing Reasoning Accuracy and Efficiency with Stepwise Adaptive Thinking](https://mlsanity.com/paper/2604.07922/) (2026)
- [When Can LLMs Learn to Reason with Weak Supervision?](https://mlsanity.com/paper/2604.18574/) (2026)
- [ThoughtFold: Folding Reasoning Chains via Introspective Preference Learning](https://mlsanity.com/paper/2606.03503/) (2026)
- [Rethinking Faithfulness in LLMs: A Pairwise Context-Sensitive Perspective](https://mlsanity.com/paper/2610.07894/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) has markedly improved the performance of Large Language Models (LLMs) on tasks requiring multi-step reasoning. However, most RLVR pipelines rely on sparse outcome-based rewards, providing little supervision over intermediate steps and thus encouraging over-confidence and spurious reasoning, which in turn increases hallucinations. To address this, we propose FaithRL, a general reinforcement learning framework that directly optimizes reasoning faithfulness. We formalize a faithfulness-maximization objective and theoretically show that optimizing it mitigates over-confidence. To instantiate this objective, we introduce a geometric reward design and a faithfulness-aware advantage modulation mechanism that assigns step-level credit by penalizing unsupported steps while preserving valid partial derivations. Across diverse backbones and benchmarks, FaithRL consistently reduces hallucination rates while maintaining (and often improving) answer correctness. Further analysis confirms that FaithRL increases step-wise reasoning faithfulness and generalizes robustly. Our code is available at https://github.com/aintdoin/FaithRL.